The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. LOADING... Click the icon to view the data table. Specimen Steel ball Diamond 1 50 52 2 57 56 3 61 61 4 71 74 5 68 69 6 54 56 7 65 68 8 51 51 9 53 56 Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'. The lower bound is nothing. The upper bound is nothing. (Round to the nearest tenth as needed.) State the appropriate conclusion. Choose the correct answer below. There is sufficient evidence to conclude that the two indenters produce different hardness readings. There is insufficient evidence to conclude that the two indenters produce different hardness readings.

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Description: The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of dif

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids

Section: Chapter Questions

Problem 79A

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The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements.

Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Click the icon to view the data table.
Specimen Steel ball Diamond
1 50 52
2 57 56
3 61 61
4 71 74
5 68 69
6 54 56
7 65 68
8 51 51
9 53 56

Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'.

The lower bound is

nothing.

The upper bound is

nothing.

(Round to the nearest tenth as needed.)

State the appropriate conclusion. Choose the correct answer below.

There is sufficient evidence to conclude that the two indenters produce different hardness readings.

There is insufficient evidence to conclude that the two indenters produce different hardness readings.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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